

from typing import List, Optional, Tuple, Union

import torch

from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class 					__lowercase  (						_SCREAMING_SNAKE_CASE				):





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       int:
														super().__init__()

														# make sure scheduler can always be converted to DDIM
														A      :					List[str]      		=					DDIMScheduler.from_config(scheduler.config						)

														self.register_modules(unet=__UpperCAmelCase    ,						scheduler=__UpperCAmelCase						)






							@torch.no_grad()
							def __call__(					self    ,						__UpperCAmelCase = 1    ,						__UpperCAmelCase = None    ,						__UpperCAmelCase = 0.0    ,						__UpperCAmelCase = 50    ,						__UpperCAmelCase = None    ,						__UpperCAmelCase = "pil"    ,						__UpperCAmelCase = True    ,						)		->       Union[ImagePipelineOutput, Tuple]:

														# Sample gaussian noise to begin loop
														if isinstance(self.unet.config.sample_size    ,						__UpperCAmelCase						):
																					A      :					List[str]      		=					(
																					    batch_size,
																					    self.unet.config.in_channels,
																					    self.unet.config.sample_size,
																					    self.unet.config.sample_size,
																					)
														else:
																					A      :					Dict      		=					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

														if isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						) and len(__UpperCAmelCase						) != batch_size:
																					raise ValueError(
																					    f'You have passed a list of generators of length {len(__UpperCAmelCase						)}, but requested an effective batch'
																					    f' size of {batch_size}. Make sure the batch size matches the length of the generators.'						)

														A      :					str      		=					randn_tensor(__UpperCAmelCase    ,						generator=__UpperCAmelCase    ,						device=self.device    ,						dtype=self.unet.dtype						)

														# set step values
														self.scheduler.set_timesteps(__UpperCAmelCase						)

														for t in self.progress_bar(self.scheduler.timesteps						):
																					# 1. predict noise model_output
																					A      :					Optional[int]      		=					self.unet(__UpperCAmelCase    ,						__UpperCAmelCase						).sample

																					# 2. predict previous mean of image x_t-1 and add variance depending on eta
																					# eta corresponds to η in paper and should be between [0, 1]
																					# do x_t -> x_t-1
																					A      :					Optional[Any]      		=					self.scheduler.step(
																					    __UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						eta=__UpperCAmelCase    ,						use_clipped_model_output=__UpperCAmelCase    ,						generator=__UpperCAmelCase						).prev_sample

														A      :					Dict      		=					(image / 2 + 0.5).clamp(0    ,						1						)
														A      :					Dict      		=					image.cpu().permute(0    ,						2    ,						3    ,						1						).numpy()
														if output_type == "pil":
																					A      :					Tuple      		=					self.numpy_to_pil(__UpperCAmelCase						)

														if not return_dict:
																					return (image,)

														return ImagePipelineOutput(images=__UpperCAmelCase						)









from math import factorial







class 					__lowercase  :





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Optional[int]:
														A      :					Union[str, Any]      		=					real
														if isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					str      		=					[1] * rank
														else:
																					A      :					Dict      		=					rank




							def __repr__(					self						)		->       List[str]:
														return (
														    f'{self.real}+'
														    f'{"+".join(str(__UpperCAmelCase						)+"E"+str(n+1						)for n,dual in enumerate(self.duals						)						)}'
														)




							def       snake_case			(					self						)		->       Union[str, Any]:
														A      :					List[Any]      		=					self.duals.copy()
														while cur[-1] == 0:
																					cur.pop(-1						)
														return Dual(self.real    ,						__UpperCAmelCase						)




							def __add__(					self    ,						__UpperCAmelCase						)		->       Any:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					return Dual(self.real + other    ,						self.duals						)
														A      :					int      		=					self.duals.copy()
														A      :					Any      		=					other.duals.copy()
														if len(__UpperCAmelCase						) > len(__UpperCAmelCase						):
																					o_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														elif len(__UpperCAmelCase						) < len(__UpperCAmelCase						):
																					s_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														A      :					List[str]      		=					[]
														for i in range(len(__UpperCAmelCase						)						):
																					new_duals.append(s_dual[i] + o_dual[i]						)
														return Dual(self.real + other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__add__




							def __sub__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														return self + other * -1




							def __mul__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Union[str, Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i * other						)
																					return Dual(self.real * other    ,						__UpperCAmelCase						)
														A      :					Optional[Any]      		=					[0] * (len(self.duals						) + len(other.duals						) + 1)
														for i, item in enumerate(self.duals						):
																					for j, jtem in enumerate(other.duals						):
																												new_duals[i + j + 1] += item * jtem
														for k in range(len(self.duals						)						):
																					new_duals[k] += self.duals[k] * other.real
														for index in range(len(other.duals						)						):
																					new_duals[index] += other.duals[index] * self.real
														return Dual(self.real * other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__mul__




							def __truediv__(					self    ,						__UpperCAmelCase						)		->       Optional[int]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Optional[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i / other						)
																					return Dual(self.real / other    ,						__UpperCAmelCase						)
														raise ValueError




							def __floordiv__(					self    ,						__UpperCAmelCase						)		->       Union[str, Any]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					List[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i // other						)
																					return Dual(self.real // other    ,						__UpperCAmelCase						)
														raise ValueError






							def __pow__(					self    ,						__UpperCAmelCase						)		->       Any:
														if n < 0 or isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					raise ValueError('''power must be a positive integer'''						)
														if n == 0:
																					return 1
														if n == 1:
																					return self
														A      :					Dict      		=					self
														for _ in range(n - 1						):
																					x *= self
														return x






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_		):
							if not callable(lowerCamelCase_		):
														raise ValueError('''differentiate() requires a function as input for func'''		)
							if not isinstance(lowerCamelCase_     ,				(float, int)		):
														raise ValueError('''differentiate() requires a float as input for position'''		)
							if not isinstance(lowerCamelCase_     ,				lowerCamelCase_		):
														raise ValueError('''differentiate() requires an int as input for order'''		)
							A      :					Any      		=					Dual(lowerCamelCase_     ,				1		)
							A      :					Dict      		=					func(lowerCamelCase_		)
							if order == 0:
														return result.real
							return result.duals[order - 1] * factorial(lowerCamelCase_		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()






		def        snake_case__		(    lowerCamelCase_		):
									return y**2 * y**4

		print(differentiate(f, 9, 2))






